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Square Roots Modulo p

  • Gonzalo Tornaría
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2286)

Abstract

The algorithm of Tonelli and Shanks for computing square roots modulo a prime number is the most used, and probably the fastest among the known algorithms when averaged over all prime numbers. However, for some particular prime numbers, there are other algorithms which are considerably faster.

In this paper we compare the algorithm of Tonelli and Shanks with an algorithm based in quadratic field extensions due to Cipolla, and give an explicit condition on a prime number to decide which algorithm is faster. Finally, we show that there exists an infinite sequence of prime numbers for which the algorithm of Tonelli and Shanks is asymptotically worse.

Keywords

Prime Number Arithmetic Progression Discrete Logarithm Absolute Constant Explicit Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Gonzalo Tornaría
    • 1
  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA

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